My job involves analyzing air pollutant emission estimates. I have a dataset of 5 timeseries, for which I would like to both backcast and forecast aggregate statistics (e.g. a range of expectation for the sum of emissions in a future year).
One interesting feature is that each series (as a unit) may be offset by either 0 or -6 months from the calendar year. Another is that about 10-20% of observations are missing. A third interesting property is that the data provider is willing to "guarantee" each datapoint to "5%".
If I'm willing to assume, for the purposes of approximation, that:
- the missingness is MAR; and
- the "5%" error is uniform or Beta
... are there tools or approaches that can be combined to do a reasonable job of bounding the magnitude and direction of the expected next annual (calendar-year) average of all 5 series?
In response to comments and questions thus far:
Thanks for the feedback! I'll be able to respond more frequently on Monday.
There is definitely correlation both within and between the series, and there are mechanistic explanations for both kinds of correlation. Each series corresponds to a petroleum refinery. They have large, although varying by a factor of 2-3x, capital investments and (all) respond to changing local & global market demand. There is some specialization in the slate of products generated by each one; for this and other reasons, the market competition is not "perfect". To the extent possible, I'd like to focus on estimating the correlation strictly from the data.
There are 7 observations within each series — each corresponds to a 12-month interval from (ignoring offsets) 2008--2014.
There are likely "period" effects on scales ranging from super-annual to sub-annual, but hard to be definite about the scales of periodicity (unless you are an oil market expert, in which case, please weigh in!)
The "5% guarantee" is not publicly described in technical detail. Mentioned in XLS here: http://www.arb.ca.gov/cc/reporting/ghg-rep/reported-data/ghg-reports.htm (I'll post raw data on Monday). I think I'm willing to assume for the purposes of a first approximation that there are/were "true, unobserved" values within 5% of the observed in each and every case.
There is exogenous (non-quantitative; think newspaper articles) evidence of shocks to individual series resulting from, e.g. accidental or planned disruptions / downtime (like equipment upgrades); for the purposes of a first approximation I wish to exclude these from consideration.
I'm looking right now at Rob Hyndman's work. I'm an advanced R programmer, but a known non-expert in forecasting.